Question

Weekly demand for a particular item averages 30 units, with a standard deviation of 4. This item is managed with a fixed-order-interval model. The order interval is three weeks, and this item has a certain lead time of one week. The desired service level is 97.5 percent. Assume that it is now time to place another order, and there are 43 units on hand. How many units should be ordered?

A. 63
B. 93
B. 83
D.None of the above

Answer 1

(B)93

Explanation:

Since we are using a fixed-order-interval model,

The Amount to Order=Expected Demand During protection Interval+Safety Stock-Amount at Hand

[TeX]=d(OI+LT)+z\sigma_{d}\sqrt{OI+LT}-A[/TeX]

Where:

d=weekly demand

OI=Order Interval

LT=Lead Time

z=Standard Deviation of Desired Service Level

[TeX]\sigma_{d}[/TeX]=Standard Deviation of weekly Demand

A= Amount at Hand

[TeX]=d(OI+LT)+z\sigma_{d}\sqrt{OI+LT}-A[/TeX]

[TeX] [30(3 + 1)] + [1.964*4*\sqrt{3 + 1} - 43[/TeX]

[TeX] = 120 + 15.712 - 43 = 92.7[/TeX]